# A rectangular metal manhole with an area of 0.5m^2 is situated a long cemented pathway. the leght of the pathway is 8m longer Than its width

1
by elamae19

2015-06-10T13:24:33+08:00

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We let the width be x, this would make the length x+8. So:
Area = length*width
0.5 = (x+8)x
0.5 = x²+8x
0 = x²+8x-0.5
0 = 2x²+16x-1

x = -16 ± √(16²+8) = -16 ± √(256+8) = -16 ± √264 = -16 ± 2√66 = -4 ± √66
4                        4                     4                  4                   2
We cannot have a negative value so we only consider -4 + √66
2

Therefore the width is √66 - 4 m and the length is √66 + 4 m
2                                      2

Check:
[√66/2 - 4][√66/2+4] ≟  0.5
Notice that this is the difference of two squares so:
(√66/2)² - 4² ≟ 0.5
66/4 - 16 ≟ 0.5
[66-(4*16)]/4 ≟ 0.5
66-64 = 0.5*4
2 = 2  TRUE